I think the constant non-zero skip rate throughout the entire song length is explained by people who would have skipped the song at the beginning but who weren'

I think the constant non-zero skip rate throughout the entire song length is explained by people who would have skipped the song at the beginning but who weren't present when the song started (e.g. they went to the kitchen to get a drink). These people would skip the song as soon as they get back, which could be at any point within the song.